We have studied the quasiparticle excitation spectrum of the superconductor Ba8Si46 by local tunneling spectroscopy. Using high energy resolution achieved in Superconductor-Superconductor junctions we observed tunneling conductance spectra of a non-conventional shape revealing two distinct energy gaps, DeltaL = 1.3meV and DeltaS = 0.9meV. The analysis of tunneling data evidenced that DeltaL is the principal superconducting gap while DeltaS, smaller and more dispersive, is induced into an intrinsically non-superconducting band of the material by the inter-band quasiparticle scattering.